{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Diffusion Model (BPS 1987)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from numpy import random\n",
    "import math\n",
    "import matplotlib.pyplot as plt\n",
    "from numpy import cumsum, log, polyfit, sqrt, std, subtract\n",
    "from numpy.random import randn\n",
    "from scipy.optimize import curve_fit\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def update_market(N, buyers, sellers, price, price_max, buyer_pos, seller_pos, transaction_found):\n",
    "    # N is the number of noise traders in the market\n",
    "    # price_max is the price upper bound\n",
    "    #seller_pos (buyer_pos) gives the position of the seller (buyer) who participates in a transaction\n",
    "\n",
    "    \n",
    "    # This functions allows to update the bids and asks at a time step.\n",
    "    # Return: the updated buyers prices and sellers prices\n",
    "    \n",
    "    for b in range (int(N/2)):\n",
    "        if buyers[b] == 0:\n",
    "            buyers[b] = random.randint(0,2,1)[0]\n",
    "        elif buyers[b] == price_max:\n",
    "            buyers[b] = price_max - random.randint(0,2,1)[0]\n",
    "        else:\n",
    "            buyers[b] = buyers[b] + 2*random.randint(0,2,1)[0] - 1\n",
    "    for s in range (int(N/2)):\n",
    "        if sellers[s] == 0:\n",
    "            sellers[s] = random.randint(0,2,1)[0]\n",
    "        elif sellers[s] == price_max:\n",
    "            sellers[s] = price_max - random.randint(0,2,1)[0]\n",
    "        else:\n",
    "            sellers[s] = sellers[s] + 2*random.randint(0,2,1)[0] - 1\n",
    " \n",
    "    if transaction_found:\n",
    "        buyers[buyer_pos] = random.randint(0, price + 1, 1)[0]\n",
    "        sellers[seller_pos] = random.randint(price, price_max + 1, 1)[0]\n",
    "        \n",
    "    return(buyers, sellers)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def diffusion_Model(N, price_max, T):\n",
    "    \n",
    "    # This function initializes and implements the diffusion Model with N noise agents and a price_max for T time steps\n",
    "    # Returns: the prices at each time step and the final distribution of prices\n",
    "    # If there is no transaction at time t, the price at t is -1\n",
    "    \n",
    "    \n",
    "    # N is the number of noise traders in the market\n",
    "    # price_max is the price upper bound\n",
    "    # T is the max time step\n",
    "    \n",
    "    # buyers (sellers) list contains the prices offered by the buyers(sellers) at one time step\n",
    "    buyers = []\n",
    "    sellers = []\n",
    "    \n",
    "    # prices[t] is the price at which a transaction occurred at time t\n",
    "    prices = []\n",
    "    \n",
    "    # N has to be an even number to have the same number of buyers and sellers\n",
    "    if N//2 == 1:\n",
    "        N = N + 1\n",
    "           \n",
    "    #Initialization of the market\n",
    "    buyers = random.randint(0 , price_max/2 , int(N/2) )\n",
    "    sellers = random.randint(price_max/2 , price_max + 1 , int(N/2) )\n",
    "    agents = np.concatenate((buyers, sellers))\n",
    "    \n",
    "    fig = plt.gcf()\n",
    "    fig.set_size_inches(18.5, 10.5) \n",
    "    plt.hist(agents, bins = 500)\n",
    "    plt.title(\"Initial price distribution for the diffusion model, N=%i et T=%i\" %(N,T))\n",
    "    plt.ylabel('Number of agents')\n",
    "    plt.xlabel('Price')\n",
    "    plt.show()\n",
    "    transactions = []\n",
    "    # price give the transaction price (if a transaction happens).\n",
    "    # If there is no transaction at t, we keep the price of t-1\n",
    "    price = int(price_max/2)\n",
    "    for t in range (T):\n",
    "        \n",
    "        #seller_pos (buyer_pos) gives the position of the seller (buyer) who participates in a transaction\n",
    "        seller_pos = -1\n",
    "        buyer_pos = -1\n",
    "        \n",
    "        #select a random seller or buyer\n",
    "        selected = random.randint(0, N, 1)[0]\n",
    "        transaction_found = False\n",
    "        if selected < int(N/2): #we have selected a buyer\n",
    "            for s in range(int(N/2)):\n",
    "                if sellers[s] == buyers[selected] and transaction_found == False:\n",
    "                    buyer_pos = selected\n",
    "                    seller_pos = s\n",
    "                    price = buyers[selected]    \n",
    "                    transaction_found = True\n",
    "                    \n",
    "        else: #we have selected a seller\n",
    "\n",
    "            for b in range(int(N/2)):\n",
    "                if buyers[b] == sellers[selected - int(N/2)] and transaction_found == False:\n",
    "                    buyer_pos = b\n",
    "                    seller_pos = selected - int(N/2)\n",
    "                    price = buyers[b]\n",
    "                    transaction_found = True\n",
    "\n",
    "        \n",
    "        prices.append(price)\n",
    "        if transaction_found:\n",
    "            transactions.append(price)\n",
    "        buyers, sellers = update_market(N, buyers, sellers, price, price_max, buyer_pos, seller_pos, transaction_found)\n",
    "    \n",
    "    return(prices, np.concatenate((buyers, sellers)), transactions)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1b850fc82e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Defining the model parameters\n",
    "N = 500\n",
    "price_max = 250\n",
    "T = 10000\n",
    "# Running the simulation\n",
    "prices, agents, transactions= diffusion_Model(N, price_max, T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1b8530476a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the Prices evolution with time\n",
    "fig = plt.gcf()\n",
    "fig.set_size_inches(18.5, 10.5) \n",
    "plt.plot(range(T),prices)\n",
    "plt.title(\"Diffusion model for T =%i, N=%i and price_max=%.1f\" %(T,N, price_max))\n",
    "plt.ylabel('Price')\n",
    "plt.xlabel('Discrete time')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1b8531c04e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the prices distribution between agents in the final configuration at T\n",
    "fig = plt.gcf()\n",
    "fig.set_size_inches(18.5, 10.5) \n",
    "plt.hist(agents, bins = 500)\n",
    "plt.title(\"Final price distribution for N=%i et T=%i\" %(N,T))\n",
    "plt.ylabel('Number of agents')\n",
    "plt.xlabel('Price')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1b8533634e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the price variation at each time interval = 1\n",
    "\n",
    "def price_variation(prices):\n",
    "    delta = []\n",
    "    for i in range (len(prices)-2):\n",
    "            delta.append((math.log(prices[i+1]) - math.log(prices[i])))\n",
    "    return delta\n",
    "\n",
    "delta_price = price_variation(prices)\n",
    "time_t = [t for t in range(len(delta_price))]\n",
    "fig = plt.gcf()\n",
    "fig.set_size_inches(18.5, 10.5) \n",
    "plt.plot(time_t,delta_price)\n",
    "plt.title(\"Return for the Diffusion model, N=%i et T=%i\" %(N,T))\n",
    "plt.ylabel('Returns')\n",
    "plt.xlabel('Discrete time')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "287\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1b8534d6be0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the returns distribution without zeros\n",
    "delta_updated = []\n",
    "for i in range(len(delta_price)):\n",
    "    if delta_price[i] != 0:\n",
    "        delta_updated.append(delta_price[i])\n",
    "print(len(delta_updated))\n",
    "fig = plt.gcf()\n",
    "fig.set_size_inches(18.5, 10.5) \n",
    "plt.hist(delta_updated, bins = 500)\n",
    "plt.title(\"Returns distribution for the Diffusion model, N=%i et T=%i\" %(N,T))\n",
    "plt.ylabel('Frequency')\n",
    "plt.xlabel('Returns')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Wall time: 15.1 s\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Asus\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:85: RuntimeWarning: divide by zero encountered in log\n"
     ]
    }
   ],
   "source": [
    "# Plot the range values of prices\n",
    "\n",
    "def create_ranges(series):\n",
    "    series.pop(0)\n",
    "    series.pop(1)\n",
    "    #return prices with different lengths of time chosen\n",
    "    p_1 = [series]\n",
    "    p_2 = [series[:T//2],series[T//2:]]\n",
    "    \n",
    "    p_4 = []\n",
    "    for i in range(4):\n",
    "        p_4.append(series[i*(T//4):(i+1)*(T//4)])\n",
    "    p_8 = []\n",
    "    for i in range(8):\n",
    "        p_8.append(series[i*(T//8):(i+1)*(T//8)])\n",
    "    p_16 = []\n",
    "    for i in range(16):\n",
    "        p_16.append(series[i*(T//16):(i+1)*(T//16)])\n",
    "    p_32 = []\n",
    "    for i in range(32):\n",
    "        p_32.append(series[i*(T//32):(i+1)*(T//32)])\n",
    "    p_64 = []\n",
    "    for i in range(64):\n",
    "        p_64.append(series[i*(T//64):(i+1)*(T//64)])\n",
    "    p_128 = []\n",
    "    for i in range(128):\n",
    "        p_128.append(series[i*(T//128):(i+1)*(T//128)])\n",
    "    p_256 = []\n",
    "    for i in range(256):\n",
    "        p_256.append(series[i*(T//256):(i+1)*(T//256)])\n",
    "    p_512 = []\n",
    "    for i in range(512):\n",
    "        p_512.append(series[i*(T//512):(i+1)*(T//512)])\n",
    "    p_1024 = []\n",
    "    for i in range(1024):\n",
    "        p_1024.append(series[i*(T//1024):(i+1)*(T//1024)])\n",
    "    p_2048 = []\n",
    "    for i in range(2048):\n",
    "        p_2048.append(series[i*(T//2048):(i+1)*(T//2048)])\n",
    "    p_4096 = []\n",
    "    for i in range(4096):\n",
    "        p_4096.append(series[i*(T//4096):(i+1)*(T//4096)])\n",
    "\n",
    "    return([p_1,p_2,p_4,p_8,p_16,p_32,p_64,p_128,p_256,p_512,p_1024,p_2048,p_4096])\n",
    "\n",
    "def range_prices(series , m):\n",
    "    #Prices is a list containing sublists\n",
    "    #m is the number of subintervals within prices\n",
    "    \n",
    "    #This first list allows to store the rescaled ranges for each subinterval before averaging them\n",
    "    rescaled_ranges = []\n",
    "    #This list will store the square mean adjusted series\n",
    "    squared_series=[]\n",
    "    \n",
    "    Y_div = []\n",
    "    Y_div_square = []\n",
    "    means = []\n",
    "    for i in range(len(series)):\n",
    "        #Calculate the prices mean for a subinterval\n",
    "        moy = np.mean(series[i])\n",
    "        #Create mean adjusted series for a subinterval\n",
    "        series[i] = series[i] - moy*np.ones((len(series[i])))\n",
    "        #Create squared mean adjusted series for a subinterval (to calculate the standard deviation)\n",
    "        squared_series = (series[i] - moy*np.ones(len(series[i])))**2\n",
    "        #Create cumulative deviate series \n",
    "        Z = []\n",
    "        for k in range (1,len(series[i])):\n",
    "            Z.append(sum(series[i][:k]))\n",
    "        #Compute the range\n",
    "        R = 0\n",
    "        if (max(Z) - min(Z)) > 0:\n",
    "            R = max(Z) - min(Z)\n",
    "        #Compute the standard deviation\n",
    "        S = 0\n",
    "        S = np.sqrt((1/len(series[i]))*sum(squared_series))\n",
    "        #Adding the rescaled range to the list before averaging\n",
    "        rescaled_ranges.append(R)\n",
    "        \n",
    "    return(np.log(np.mean(rescaled_ranges)))\n",
    " \n",
    "        \n",
    "\n",
    "\n",
    "\n",
    "def rescaled_ranges(series):\n",
    "    result = []\n",
    "    ranges = create_ranges(series)\n",
    "    for r in range(len(ranges)):\n",
    "        result.append(range_prices(ranges[r] , r+1))\n",
    "            \n",
    "    return(result)\n",
    "\n",
    "\n",
    "range_values = rescaled_ranges(prices)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1b853751588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plotting the obtained rescaled range and comparing to the theoretical results\n",
    "\n",
    "def theoretical_hurst(t,H,A,t0):\n",
    "    return(H*np.log(t)+A*np.log(np.log(t)-np.log(t0)))\n",
    "\n",
    "def theoretical_derivative(t,H,A,t0):\n",
    "    return(H+A*(1/(t-np.log(t0))))\n",
    "\n",
    "ln_t = [math.log((T-2)//(2**t)) for t in range(10)]\n",
    "\n",
    "\n",
    "popt, pcov = curve_fit(theoretical_hurst, ln_t, range_values[:10], maxfev=10000)\n",
    "\n",
    "fig = plt.gcf()\n",
    "fig.set_size_inches(18.5, 10.5) \n",
    "\n",
    "fit = [theoretical_hurst(t,popt[0],popt[1],popt[2]) for t in ln_t]\n",
    "theory = [theoretical_hurst(t,1.43,popt[1],popt[2]) for t in ln_t]\n",
    "\n",
    "plt.plot(ln_t, range_values[:10], \"ro\", label='R/S')\n",
    "plt.plot(ln_t,fit[:10], label='Fit function')\n",
    "plt.ylabel('ln(R/S)')\n",
    "plt.xlabel('ln($\\Delta$t)')\n",
    "plt.legend()\n",
    "plt.title(\"Hurst Plot for N=%i and T=%i\" %(N,T))\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[6.90659321 6.90612244 6.90651064 ... 7.35560747 7.35493759 7.3544278 ]\n",
      "Hurst(GBM):   0.4986501925766181\n",
      "Hurst(MR):    0.00022992698729606986\n",
      "Hurst(TR):    0.955781914845145\n",
      "Hurst(Diffusion):  0.35634133071369506\n"
     ]
    }
   ],
   "source": [
    "# Gives the Hurst of the price series\n",
    "def hurst(ts):\n",
    "    \"\"\"Returns the Hurst Exponent of the time series vector ts\"\"\"\n",
    "    # Create the range of lag values\n",
    "    lags = range(2, 100)\n",
    "\n",
    "    # Calculate the array of the variances of the lagged differences\n",
    "    tau = [sqrt(std(subtract(ts[lag:], ts[:-lag]))) for lag in lags]\n",
    "\n",
    "    # Use a linear fit to estimate the Hurst Exponent\n",
    "    poly = polyfit(log(lags), log(tau), 1)\n",
    "\n",
    "    # Return the Hurst exponent from the polyfit output\n",
    "    return poly[0]*2.0\n",
    "\n",
    "# Create a Gometric Brownian Motion, Mean-Reverting and Trending Series\n",
    "gbm = log(cumsum(randn(100000))+1000)\n",
    "print(gbm)\n",
    "mr = log(randn(100000)+1000)\n",
    "tr = log(cumsum(randn(100000)+1)+1000)\n",
    "\n",
    "# Output the Hurst Exponent for each of the above series\n",
    "# and the price of Google (the Adjusted Close price) for \n",
    "# the ADF test given above in the article\n",
    "print(\"Hurst(GBM):   %s\" %(hurst(gbm)))\n",
    "print(\"Hurst(MR):    %s\" %(hurst(mr)))\n",
    "print(\"Hurst(TR):    %s\" %(hurst(tr)))\n",
    "\n",
    "# Assuming you have run the above code to obtain 'goog'!\n",
    "print(\"Hurst(Diffusion):  %s\" %(hurst(prices)))"
   ]
  },
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   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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